help-0

[limpid urchin]

im trying to use the identities but i dont see one that works

[jagged imp]

its just distributing the 1/sin^2(theta) into sin^2(theta)+1

on the RHS

or alternatively factoring out 1/sin^2(theta) on the lhs

[limpid urchin]

wait im confused

is there an easier way to write this ? 🤣

ik people used the bot but im not sure how to

aw man i need to brb if im not back in time ill just re ask the qustion somewhere else if i cant solve it myslef 🤣

[velvet pelican]

$\cos^2(\theta) \left(1+\frac{1}{\sin^2(\theta)}\right) = \cos^2(\theta) \left(\frac{\sin^2(\theta)+1}{\sin^2(\theta)}\right)$

[ocean seal]

Frosty

[velvet pelican]

@limpid urchin ^

is this what you mean

[limpid urchin]

ahh on the right hand side put cos on the numerator multiplying (sin^2theta +1)

[velvet pelican]

Yes, but it's just making the same denominator, no identities required

[limpid urchin]

did i multipyly it wrong then?

[velvet pelican]

If you got the answer then no

the key idea was just to have the same denominator

[limpid urchin]

wdym

[velvet pelican]

^

just have sin^2 in the denominator

[limpid urchin]

im still confused. idk how the lhs can become rhs

do i expand the lhs and it shoul;d become rhs

[velvet pelican]

You are just saying that $1 = \frac{\sin^2(\theta)}{\sin^2(\theta)}$

[ocean seal]

Frosty

[velvet pelican]

and then adding the 2 fractions

ignoring the cos^2 term because it is multiplied by everything

[limpid urchin]

OHHH! so change the 1 in the eqation to that then multiply by 1/sin^2theta

[velvet pelican]

Yes

[limpid urchin]

Ohhh tysm u made it clear

im just super slow

and this exam is in a few days and I know i'm failing but i wanna try it atleast LMAO

[velvet pelican]

good luck

[limpid urchin]

ty

gonna need it ahha

[fathom rain]

"Amy is going to make a salad made of 3 different vegetables and she has 5 different vegetables to choose from. In how many ways can she make her salad?

I mean I thought it would be 5 * 4 * 3 but it definitely isnt

[vale wigeon]

it's that divided by 3 factorial

to account for the fact that the order in which you pick your vegetables doesnt matter

[fathom rain]

ooooh so if i make a salad made of 7 different vegetables its 7 factorial?

[vale wigeon]

"it"

you're not being precise enough in your wording

but if you had sufficiently many veggies to choose from, and you were choosing 7, then yes, you would divide by 7! to account for the order not mattering.

[fathom rain]

Alright thanks yeah I ain't the best in English

[alpine sable]

why cant i type in the bracket for the red graph 2/3x-3pi/4 to make them in sync?

[vale wigeon]

eh?

[alpine sable]

what do i type in the brackets to make the red graph in sync with the blue graph?

[jagged imp]

because that wouldn't translate it the amount that you want it to. you would need to write -2cos(2/3(x-3pi/4))

[vale wigeon]

did you want this?

[alpine sable]

@jagged imp

why do we have to factorise the 2/3 outside?

@vale wigeon thats similar to my question

why do u need to factorise 2/3 outisde the bracket for the sin graph?

[vale wigeon]

you don't 'have to' do anything...

[alpine sable]

why do u have to factorise 2/3 outside the bracket in order for both graphs to be in sync?

[vale wigeon]

.-.

[alpine sable]

do u not understand my question Ann?

[vale wigeon]

you could also write the second graph as y = -2 sin(2x/3 + pi/2)

[echo spire]

I need help I have to do the same "simulation" for the cosine function

[safe island]

^ hmm i'm interested in the solution of that as well

[vale wigeon]

find a matrix $A$ such that $M\paren{\bmqty{x\y}} = A \cdot \bmqty{x\y}$

[ocean seal]

Ann

[safe island]

you just shove values in to show that it's not linear

[sonic cave]

anyone able to help with constructing the next-state table for this problem?

[vale wigeon]

what do you mean

they give you the next-state table

[novel rose]

any idea where i fucked up

[ivory pier]

Hey hello!

Does anyone here knows how to run manim?

I already installed everything, just need to run one file

[ivory pier]

<@&286206848099549185>

[open hamlet]

what level mathematics is this group?

[oak chasm]

@open hamlet We've made it to level 89.

[harsh acorn]

can someone explain me how to solve this?

[oak chasm]

@harsh acorn Use the pigeonhole principle.

Or something along those lines.

Hmm, no that's for guaranteeing you get 2 nonyellow pairs.

The least to get 2 nonyellow pairs is if you get them in the first four chopsticks.

The least to guarantee 2 nonyellow pairs is to exhaust the yellow then use pigeonhole style reasoning.

[alpine sable]

Guys

I have a problem

Here

[oak chasm]

@alpine sable I'm not sure that this channel is open. #help-5 is open if you hurry. Read the rules in #❓how-to-get-help.

[alpine sable]

Ok

[harsh acorn]

i need to consider worst case scenario right?

[oak chasm]

OK, then you might get unlucky and get all yellows at first until the yellows are gone, right?

[harsh acorn]

isnt it the best case scenario?

[oak chasm]

You keep switching.

Do you want to do best case or worst case?

[harsh acorn]

I mean we need to consider wors case scenario but taking yellows is not the worst case

[oak chasm]

Why not?

[harsh acorn]

so worst case must be taking white or brown chops

[harsh acorn]

isnt it asks for not taking yellow ones

if we take all the yellows then we are done

or am i wrong

[oak chasm]

No, read the question again.

What kind of pairs do we want?

[harsh acorn]

pairs that are not yellow

oooh

okay okay i get it

they want us pairs of chopsticks that there are not any yellow ones

so wors case is taking yellows okay i get it now

[oak chasm]

OK, now you have all nonyellows.

The best case is 4 chopsticks.

What's the worst case?

[harsh acorn]

worst is 4 too isnt it

[oak chasm]

No, you can get WWWB or BBBW.

[harsh acorn]

or does they want us pure pairs

[oak chasm]

Oh, I'm not sure.

It doesn't say the pairs need to match colors.

So, if you don't need to match colors, 4 is fine.

If you do, you need more.

The combos for 4 sticks are WWBB, WWWB, and WBBB.

Not all are matched pairs.

[harsh acorn]

or it can be WBWB?

or BWBW

[oak chasm]

Yes, but order is irrelevant.

[harsh acorn]

oh right

[oak chasm]

That makes three combos.

What are the combos for 5 without regard to order?

Oh, I forgot.

4 sticks: WWWW, WWWB, WWBB, WBBB, BBBB.

Not all are matched pairs.

5 sticks: WWWWW, WWWWB, WWWBB, WWBBB, WBBBB, BBBBB.

Do you always have two matched pairs for all those combos?

[harsh acorn]

yes

[oak chasm]

OK, then all yellows then 5 more.

[harsh acorn]

and we should 1 more for success

[oak chasm]

No, 5 is universally successful.

[harsh acorn]

oh

[oak chasm]

(WW)(WW)W, (WW)(WW)B, (WW)W(BB), (WW)(BB)B, W(BB)(BB), (BB)(BB)B

[harsh acorn]

so answer asks for pieces not pairs answer is 9x2=18

4pair for yellow 5pair for others

[oak chasm]

No.

How many yellow chopsticks are there?

[harsh acorn]

27

[oak chasm]

No.

[oak chasm]

8 pieces is 8 chopsticks.

[harsh acorn]

oh

8

[oak chasm]

So, we get all yellow at first in worst case.

That's 8.

Then we need 5 more in worst case.

That's 8 + 5.

So, 13.

[muted rapids]

Can someone help me with this?

[oak chasm]

,rotate

[oak chasm]

@muted rapids OK, see the conditions on the far right?

[muted rapids]

Yeah

[ocean seal]

Chai T. Rex

[rancid osprey]

why is there so much text on the directions

so excessive

[muted rapids]

Our teacher wants to prepare us for the super ultra math test at the end of the year

[rancid osprey]

f(-2) = f(x)

[muted rapids]

Yeah

[rancid osprey]

are u confused about something here?

[muted rapids]

I’m just confused on how to actually solve it

[oak chasm]

^

[rancid osprey]

what happens when u plug the -2 into the x's?

[muted rapids]

I don’t really know how to set up the equation, it looks confusing on how it’s set up or begin with

[rancid osprey]

the question is telling you to Find f(-2) right

[muted rapids]

Yes

[rancid osprey]

for the Function: on the right are 2 functions they gave u

so the functions are already there

you just copy and paste it but with f(-2)

you know what x is in the function right?

[muted rapids]

Yeah ok I think I understand

Thanks

[rancid osprey]

nono

gotta make sure u know

what does f(-2) mean?

[muted rapids]

It means I plug in the -2 where the X is

[rancid osprey]

yes

[muted rapids]

Thanks

[rancid osprey]

you know what this is for?

[muted rapids]

No

[rancid osprey]

the first one is for the first function

second is for the 2nd.

once u plug in the -2 into the first function

what's ur answer?

[muted rapids]

Hold on let me solve

[rancid osprey]

yup take ur time

[muted rapids]

35?

[rancid osprey]

3(-2)^2 -1

3(-2)(-2)-1

3(4)-1

12-1

[muted rapids]

11

[rancid osprey]

yup

what does x < 1 mean to you?

[muted rapids]

X is less than 1

[rancid osprey]

is 11 less than 1?

[muted rapids]

No

[oak chasm]

11 isn't x.

x is -2.

That's why you check the conditions first.

[rancid osprey]

hmm, i must of taught him wrong then

but there's some arithmetic you gotta work on audrey

[muted rapids]

What does that mean?

[rancid osprey]

like umm, simple additions, multiplication, etc.

[muted rapids]

I usually can do that stuff pretty well this problem was just confusing me is all

[rancid osprey]

well. im gonna head out to do my assignments

hopefully chai can help you out fully 🙂

[muted rapids]

I figured it out I don’t need any more help thanks tho 🎃🌽🚽☀️🧼🏫🪂👺🥵👹🦾👮‍♀️🧑‍🌾🦸‍♀️👰🏾‍♂️🧝‍♀️🧙‍♂️🧞‍♀️🧞🧞‍♂️🧜‍♀️🧜🏿🧜‍♂️🧚‍♀️🧚🏿🧚‍♂️👼🤰🤱👩‍🍼🧖🏿‍♀️🤳🏿💆‍♂️💃🕺👯‍♀️👯👯‍♂️👩‍🦼👩‍🦽👩‍🦯👨‍❤️‍💋‍👨👩‍❤️‍💋‍👩🧶🪡👕👖🩲🩳👔👗👙🩱👘🥻🥽🪖⛑🐲🐉🌝🌈☔️🌬🍌🍆🥬🥒🍑🍊🫒🥞🧇🍺🏉🏐🏀🎽🥋⛸🛹🚵🏼🥇🎨🎼🎺🚕🏍⛴🚢🗿🗽🏔⏳🔌🕰🎞📽💎💸💶🔫💣🧲🔪🚬🛁🧽🗝🪣🎀🪄🪆🎏📯🗄📌📎🔗🖇🧷🖊✂️📍✏️❤️💜🧡🖤💛🤍💚🤎💙💔💔💔💔💔💔💔💔💔💔

[muted raft]

[naive lion]

For a non homogenous equation = 4^t what ANSATZ would you use to find the particular integral?

[harsh acorn]

@oak chasm does this question count as probability

[oak chasm]

No, it's not a probability, it's a count, which is combinatorics, I think.

[stoic verge]

can anybody help me understand how to calculate this limit

the answer is 0, as shown, but im having a hard time getting there

[wide talon]

@stoic verge n reaches inf faster than ln n

[real sinew]

So you have 1 over an increasingly large number which approaches 0

[wide talon]

so the denominator will approach inf as n approaches inf

[stoic verge]

yes, I get that intuitively. but will i get full credit on an exam if I describe it that way doe

[real sinew]

What class is it for?

[stoic verge]

i even multiplied both the numerator and denominator by n + lnn

calc 2

that even puts the denominator at n^2 - (lnn)^2, further stressing that it goes to inf

[real sinew]

If it is calc 2 you could consider L'hôpital's rule but it isnt really necessary. What GifflarN said is intuitive enough

[muted raft]

$$x-\ln(x) = \qty(x)\qty(1-\frac{\ln(x)}{x})$$

[ocean seal]

zslya

[stoic verge]

omg perfect

[real sinew]

Smart way to put it

[stoic verge]

i know the way around from here

thank you so much!!!

[muted raft]

you're welcome.

[ashen wave]

Are there any tutors on this server?

I really need help with residual plots T-T

[torpid warren]

@ping while answering

[alpine sable]

U use the fact that determinant of a matrix is same as of its transpose

so now transpose the first one

[alpine sable]

And then use the property that if 2 rows are same, then u can simply add the third rows

[lethal ore]

First transpose the second matrix @torpid warren

[torpid warren]

K trying

[muted raft]

why would you transpose the second matrix?

[alpine sable]

transpose any one of them

basically the same thing

[lethal ore]

Yea

[muted raft]

it seems much easier to just transpose the first one lol

[alpine sable]

ye mathematical illusions

[fierce rune]

Can someone help me I don’t know how to answer the question

I know that I could use binomial and Poisson distribution

[lethal ore]

It'd be better if you crop the pic before sharing @fierce rune

[torpid warren]

Got it, n is odd, thanks

[fierce rune]

it’s just 1) a I need help with

I’m not sure how it wants me to answer the question

[lime zodiac]

Use the known average to find the parameters (use the formula for E(X))

[fierce rune]

ok cool thanks

Would I just leave it as like E(x) = 1

Using poisson

[harsh acorn]

is the answer 40

[dire yarrow]

How do you find the area shaded in red? height of rectangle is 5 length is 10

[glass lichen]

by symmetry the circle portions add to 1 whole circke

[dire yarrow]

I tried to get the area of the rectangle (50), figured the radius of a circle is 2.5 so the area of a circle is 19.63. 50-19.63-19.63 and then divided that by 2

[glass lichen]

so area of triangle - area of circle

or rectangle - 2 circles then half of that

[astral hound]

@dire yarrow i saw this on youtube the other day. seems to be very similar but just slightly different values https://www.youtube.com/watch?v=xnE_sO7PbBs&t=469s

[pallid bough]

That video looks right, well done @astral hound

[glass lichen]

despite it's a different area

since the bottom left corner isnt included

[pallid bough]

teaches the same principles tho

should suffice

[astral hound]

@glass lichen at the beginning of the video he does the one being asked

[harsh acorn]

my question

[dire yarrow]

so was my method correct here? (50-19.63-19.63)/2 = 5.37

[glass lichen]

Yeah havent watched the video in ages

[glass lichen]

I mean leave it exact, but looks like it

[dire yarrow]

exact?

[glass lichen]

yeah, no decimal

[dire yarrow]

but why less precise

[pallid bough]

Hello everyone, how would I go about to calculate the sum of residues? I know the poles are 4+/-7i and the residue values are 5 and -2, and that the final answer is 6πi, and not sure how to go about calculating the sum of residues

[glass lichen]

how is being exact less precise. . .

[ocean seal]

moshill1

[pallid bough]

pi is less precise then 3.14

[glass lichen]

bruh pi has infinitely more precision on the value of pi than 3.14

cause pi is pi

[dire yarrow]

ok snarky nerds, but thanks for the help, it is appreciated

[pallid bough]

i was testing the bot

apologize

[harsh acorn]

help please

[alpine sable]

is it not just 5x4x2?

[pallid bough]

man I'm gonna be honest with you, I've been studying math for four years at university level and don't know

@alpine sable I've asked @astral hound and he agreed with you

[glass lichen]

How many ways can you place the 5 math books in the 11 spaces?

[harsh acorn]

55?

[glass lichen]

No

Take it slow, let's start with the 1st book. I need to place 1 book in 1 of 11 spots, how many places can I put the book?

[glossy current]

Don't mind me using ∫ 😎

[glass lichen]

Clearly there are 11 places the 1st math book could go

[glossy current]

Those viral problem about calculating area can be solved easily with calculus but idk if it is called cheating for lower grades

[pallid bough]

Please help

[glass lichen]

channel is in use

[glass lichen]

@harsh acorn that make sense?

[harsh acorn]

11 space ofc

yep it does

[glass lichen]

right, so what about the 2nd space?

[harsh acorn]

10

3rd 9

[glass lichen]

and then 9, 8 and 7

[harsh acorn]

and goes on

[glass lichen]

right, so we can write that as $\frac{11!}{6!}$

[ocean seal]

moshill1

[harsh acorn]

oh right i get it that

[glass lichen]

where $n! = n(n-1)(n-2)...(2)(1),n\in\mathbb{N}$

[ocean seal]

moshill1

[glass lichen]

Ok so we have the math books in the 5 spaces

how many options for the 1st whatever the 2nd type of book is

chinese books

in use

[harsh acorn]

$$11!/5!+10!/4!+ 9!/2!$$?

[pallid bough]

@alpine sable I posted a question after @harsh acorn , also sorry for interrupting @glass lichen

[ocean seal]

Hyl1s

[glass lichen]

No

[harsh acorn]

oh we need to multiply them?

[glass lichen]

if we have the 5 math books in already, then the chinese books reduce to the same problem, just with 6 spaces for 4 books

[harsh acorn]

oh so $$\frac{11!}{5!}\frac{6!}{4!}\frac{2!}{2!}$$

[ocean seal]

Hyl1s

[harsh acorn]

or we should add them?

[glass lichen]

6*5*4*3 = 6!/2!

not 6!/4!

[harsh acorn]

but there are 11 space and books take 5 and 6 left why is it 6!/2!

im confused

[glass lichen]

cause you have 6 spaces remaining after the 5 math books are in right?

so the 1st chinese book has 6 options, 2nd has 5, 3rd has 4, and 4th has 3

so 6*5*4*3

[harsh acorn]

oh all right

[glass lichen]

and easy to check that equals 6!/2!

[harsh acorn]

$$\frac{11!}{5!}\frac{6!}{2!}\frac{2!}{2!}$$

[ocean seal]

Hyl1s

[harsh acorn]

ik how to do btw

[glass lichen]

oof sorry I forgot one thing (Im self taught with perms and combs sorry)

so when we placed the 5 math books, I can re-arrange the 5 books themself, so I need to divide by the numbers of ways to arrange the 5 books, which is 5!

so the 1st thing should be $\frac{11!}{6!5!}$

[ocean seal]

moshill1

[glass lichen]

since every arrangement of the 5 books looks the same, we overcounted by a factor of the total ways to arrange them

Number of ways to place the 5 math books $=\frac{11!}{6!\cdot 5!}$

[ocean seal]

moshill1

[harsh acorn]

ooh alright

[glass lichen]

so then we still have 6!/2! ways to place the chinese books, but 4! ways to arrange the books themselves, so it becomes 6!/(2!4!)

[harsh acorn]

then
$$\frac{11!}{6!\cdot5!}\cdot\frac{6!}{4!\cdot2!}\cdot\frac{2!}{2!}$$

[ocean seal]

Hyl1s

[harsh acorn]

last one does not matter

0! = 1

[glass lichen]

Yeah

and that simplifies to $\frac{11!}{5!4!2!}$

[ocean seal]

moshill1

[glass lichen]

and hopefully you recognize the final numbers from the question

[harsh acorn]

which textbook did u used for perms and combs? offtopic but i need it :d

[glass lichen]

Just randomly doing questions online

[harsh acorn]

@glass lichen can u help me for this too?

someone explained me and i did not get it so good

[jagged summit]

Can someone help me on this problem

[pallid bough]

w8 can I get mine answered before you @harsh acorn

[glass lichen]

Yeah I'm not good with those problems

[pallid bough]

@jagged summit I posted a question before

[harsh acorn]

kk

[pallid bough]

Please guys, I have an exam tomorrow and this question is one I don't understand, could I get help please 😿

[analog coral]

so this limit will give us infinity and we are to find b from y =mx+b to find asymptote. but any ways b= infinity, could you say that b = 0, so y=mx ?

i mean y = mx+infinity seems weird

[manic quail]

Could you tell us the original function, @analog coral ?

[manic quail]

And you want to find oblique asympotes?

[analog coral]

ye

[manic quail]

divide the function by x first, and calculate the limit.

[analog coral]

so this is b

[manic quail]

then you get the slope of the asympote

[analog coral]

yeyey we are to calculate b here

[manic quail]

You have to find m first.

or you can't find b.

[analog coral]

m = -1

[manic quail]

okay

[analog coral]

wdym

[manic quail]

I can't read, sorry.

[analog coral]

:p

i can't math 50/50 here haha xD

[manic quail]

If the thing goes to infinity, there shouldn't be an asymptote, I thought.

You can try "as x goes to -\infty", and see if there is one there.

[analog coral]

well ann said that there is two asymptote y=-x, y=-x-4

[analog coral]

-inf?

[manic quail]

$-\infty$

[ocean seal]

𝔙eryhappyperson

[analog coral]

yes we get -inf

when it goes towards -inf

[manic quail]

Are you sure? I haven't checked the limit.

[analog coral]

what wrong did I do

[manic quail]

You forgot the x^2 xD

in the numerator

@analog coral

[analog coral]

oh

[prisma geyser]

what's the domain of this function?

the answer^

[oak chasm]

@prisma geyser Well, the square root can only take nonnegative inputs.

The denominator can't be zero.

[prisma geyser]

i know

but the answer doesnt match

😒

[dusk smelt]

set thr denominator to be greater than 0 and solve

[oak chasm]

OK, so when does a square root match zero?

[prisma geyser]

:*

[oak chasm]

When its input is what?

[prisma geyser]

x^2+y^2-4x>0

[prisma geyser]

when x^2+y^2=4x?

[oak chasm]

Yes, but when its input is zero.

So the square root input has to be nonnegative (or else you'll get complex numbers) and nonzero (or else you'll get a zero denominator), so it has to be positive.

[dusk smelt]

complete the square for the x

[ocean seal]

Chai T. Rex

[prisma geyser]

oh

i get it, thanks

[devout socket]

Can anyone help me with some geometry

Wait what

[oak chasm]

<@&268886789983436800>

[alpine sable]

Anyone know how to do this

[devout socket]

<@&268886789983436800>

[night geyser]

thanks

[glass lichen]

They really chose their first message to be violence huh

[pallid bough]

wow what was that lol

[devout socket]

This is some g8 stuff btw

I'm really bad at geometry

Algebra Is easy

[oak chasm]

,rotate

[devout socket]

Did I even do the figure right?

[oak chasm]

Yes, the figure is right, but I can't help with geometry proofs, unfortunately.

[devout socket]

U don't have to give the answer

Just like the stuff I need to do

And I'd write the proof

[oak chasm]

I haven't done geometry proofs in about 27 years.

[glossy current]

O

I think to prove thr 5.1" you just need to prove 2 =∆

[devout socket]

I wanna say es and lt are equal since they are both altitudes on the equal sides of an isosceles triangle

[oak chasm]

I mean, all the things there are obviously true, but I don't know how to prove them.

[devout socket]

Yea same

The lessons is about congruent triangles

But idk how

[glossy current]

Ok so

∆BSL=∆BTE

[oak chasm]

OK, well triangle SEL has a right angle and shares an angle with the larger triangle

[glossy current]

BL=BE

[devout socket]

Oh shi

[glossy current]

They share ∠B

[oak chasm]

Triangle TEL has the same two angles.

[devout socket]

I didn't see those triangles

[glossy current]

and the 90° degree

Done

[oak chasm]

So, by AAS, can you prove it?

[devout socket]

We have learnt ha and hs

Ok lemme wrote the proof

[glossy current]

The only question I'd like to ask is why they don't name ∆ABC and two heights BD and CE 🤔

[devout socket]

How do I say b is a angle which is shared by both

I wrote BL=BE (effect of isosceles triangle)

That the hypotenuse

Now I need B

I say B is a common angle of both triangles

B is the vertex of isosceles bel which the other triangles are in so B is a common angle?

Nvm

[quick talon]

what is y= -3/4x + 6 in the form Ax + By + c = 0 (standard form)

[manic quail]

You probably lost an "x" there.

[quick talon]

yeah lol sorry

fixed

[manic quail]

You have to get all the terms on the left side.

[quick talon]

ok so opposite opperations

[manic quail]

yes

[quick talon]

bet

ill do it

[manic quail]

Great xD

[quick talon]

tell me if im right thop

[manic quail]

sure

[loud mauve]

im rly sorry but could anyone help w this ?

[quick talon]

is it 3x + 4y -24 = 0

???

[manic quail]

$\frac{3}{4}x+1y-6=0$

[ocean seal]

𝔙eryhappyperson

[quick talon]

what that

am i right?

[manic quail]

Yes

[quick talon]

3x + 4y -24 = 0

this???

[manic quail]

Yes.

That's right too.

[quick talon]

whats this

oh

[manic quail]

The same thing.

[quick talon]

u sure?

[manic quail]

Yes.

[quick talon]

ok

[manic quail]

You just multiplied by 4.

[quick talon]

ye

what do i do for

[manic quail]

I have never done something like this, but is there a reason you can't just differentiate implicitly?

[manic quail]

I don't know what you did it for?

[loud mauve]

sorry aa i sent the wrong question ashd one sec

[manic quail]

xD Okay

[quick talon]

Determine the equasion of a line parallel to -6x+3y= -18 with the same x intercept as the line defined by 14x +7y-14 =0

[manic quail]

Just plug in u instead of x?

[dusk smelt]

plug in the given equation instead of x

[upbeat compass]

wat it 1+1?

[manic quail]

0!+1

[dusk smelt]

and simplify it interms of u

[quick talon]

@manic quail ?

[upbeat compass]

ok thank u

[quick talon]

bro I seriouly need help

Determine the equasion of a line parallel to -6x+3y= -18 with the same x intercept as the line defined by 14x +7y-14 =0

[manic quail]

For this, you could first calculate the x intercept.

[quick talon]

how

[dusky basin]

what is experimental proability i forgot

[manic quail]

set y=0 and then solve for x

[quick talon]

on what equasion the frist or 2nd

[manic quail]

the second one, because you want the x intercept of the second one.

[loud mauve]

but p and q ?? idk how to find them or where they are

[quick talon]

k

[manic quail]

You get p and q by putting it into your "substitution equation". But does that even matter?

[loud mauve]

it's,, part of the question ?

[manic quail]

They don't ask for p and q, do they?

[loud mauve]

they literally do

[manic quail]

Ah, I cannot read, sorry.

[loud mauve]

no it's ok ! dw

[manic quail]

Just plug them in the equation.

[loud mauve]

plug,, what in

how do i find p and q based on that

[manic quail]

x=u^2+1

[quick talon]

@manic quail is x = 1 \

??

[manic quail]

10=u^2+1, for the upper one @loud mauve

[loud mauve]

but how would that give me p and q :')

[quick talon]

????

what now ??]

@manic quail

[manic quail]

Determine the slope of the first equation.

[quick talon]

ok

like y= mx +b??

[manic quail]

yes.

get it into that form and read m

[manic quail]

Do you see what I meant?

plug your limits of integration, or whatever they're called, into your substitution equation.

[quick talon]

ok i got m and now what

i have the x intercept and the slope

[manic quail]

m=2, right?

[quick talon]

i got -2

but i forgot about negative rules

[manic quail]

it's 2.

[quick talon]

i know

so now what

[manic quail]

now you know your line looks like $y=2x+c$, and you plug in your point (the intercept you found) now

[ocean seal]

𝔙eryhappyperson

[manic quail]

$0=2(1)+c$

[ocean seal]

𝔙eryhappyperson

[quick talon]

is the point c

[manic quail]

solve for c, and we are done.

[quick talon]

or no

[manic quail]

then point is (0,1)

the first is the x component, the second one the y component.

[quick talon]

is it the same c as before, -6

[manic quail]

Just solve that equation.

$0=2(1)+c$

[ocean seal]

𝔙eryhappyperson

[manic quail]

it's a different c

do -2 on both sides, and you get c=-2

[quick talon]

is it y= 2x -2

[manic quail]

Therefore $y=2x-2$ is the parallel line.

yep

[ocean seal]

𝔙eryhappyperson

[alpine sable]

Can i get help

If this isnt busy

[quick talon]

cool thx

[glossy current]

Sorry for late response but you can write B

When you referring to all angles at B, it's just ∠B in that shape

[glossy current]

Draw triangle PNQ

and maybe call I is the intersection point of PQ and NO
Now you can solve it

[alpine sable]

So

Am i doing the theroem

@glossy current

[glossy current]

Yes

[alpine sable]

so

12 squared

Then 9 sqaured

[glossy current]

Yes

I mean that's their idea

9 12 and 15 are Pythagorean triplet

It's a good way to determine how to solve btw

like u don't know how to solve, but then you realize the triplet

[alpine sable]

im confused

I get 15

For an answer

But

Thats not my choices

[glossy current]

Don't you already have ∆PNQ

no u haven't solved it done

[alpine sable]

Oh

I dont think i have pnq

[glossy current]

If PQ is 9, so PI would be a half of it

as I is the intersection point can you imagine

[alpine sable]

So 3?

[glossy current]

...

[alpine sable]

O

Wait

do u mean pie

[glossy current]

$\frac{9}{2}≠3$

[ocean seal]

Darkness

[glossy current]

@alpine sable notice that PN=PQ=R as well

[alpine sable]

mhm

[glossy current]

Since those are congruent circles, they would share the radius. Hence $PN=PO=R=12m$

[ocean seal]

Darkness

[alpine sable]

okayy

[glossy current]

On the other hand, $PI=\frac{PQ}{2}=4.5m$

[alpine sable]

Im still a bit confused

[ocean seal]

Darkness

[glossy current]

Notice that, $∆OPI$ is a right triangle at I, which you can apply the theorem to find OI

[ocean seal]

Darkness

[alpine sable]

Ok

[glossy current]

and $ON=2OI$

[ocean seal]

Darkness

[alpine sable]

so 2 times

Whatever i get?

[glossy current]

Don't they ask ON

[alpine sable]

erm

NO

yh

They ask for NO

[glossy current]

What's the difference between NO and ON. We are not talking about vectors 🗿

[alpine sable]

oh

Sorry mb

[fresh marten]

if the complex envelope of my transfer function is a sinc function, how do i convert that to standard time-domain representation

[viscid yacht]

Is this channel open

Question 1

Its practice for my regebts

[fresh marten]

whats the difference between each term in the sequence

[viscid yacht]

Uhh

Is it geometric or arithmetic

[fresh marten]

you tell me

is the difference constant or changing

[viscid yacht]

Hmm

I think its constatlnt

By -4

[fresh marten]

yup so that means its arithmetic right?

[viscid yacht]

Mhm

[fresh marten]

good

so if your difference is -4, isn't that the slope

[viscid yacht]

So formula to find 6 term?

[fresh marten]

you need to find the function where plugging 6 into x gives -24

which of the options gives that

[viscid yacht]

Oh okay

Hmm

Okay i got it

[fresh marten]

good

[viscid yacht]

Is that right

@fresh marten

[fresh marten]

yup good work

[viscid yacht]

Okay i need help on question 4

3

Question 3

@fresh marten

[plush kestrel]

you should begin with rearranging the question to make the RHS = 0

[viscid yacht]

I did this so far

[plush kestrel]

good job although im not sure on the approach you want to use since there are many

[viscid yacht]

Im factoring

[plush kestrel]

but the way i do these are first i would multiply the co-efficient of x^2 and x^0

whcih are 3 and -4

which is -12

[viscid yacht]

Wha

Can you show it worked put

Out

[plush kestrel]

you multiply the 3 and -4 first

so you get -12

[viscid yacht]

Wdym

Where donyou place those numbers

[plush kestrel]

and then finf actors of -12 whcih sum up to -11

[plush kestrel]

lets do 1 step at a time first

[viscid yacht]

What

Mkay ty

@plush kestrel

[plush kestrel]

hmmm

tyring to think how to best explain it

[viscid yacht]

Of you can show it on paper thats best

[plush kestrel]

the way i do it can be quiet complicated tbh

maybe its best for someone else to try explain it

[viscid yacht]

Okay

[lethal ore]

can I see the question, too tired to scroll up

[whole wind]

Can someone explain to me how to do this thanks

[midnight geyser]

First of all you need to find the angle with the ground and the ladder

[lethal ore]

Use cosine rule @whole wind

[midnight geyser]

the adjacent length of the angle over the Lea the of the hypotenuse is 4/20=1/5

[distant bay]

can I also ask chemistry questions in this server

[loud mauve]

hi im getting no answers and i posted this before but me and another worked on this but i still dont know what to write down, id rly appreciate any help !

[midnight geyser]

First of all it might be helpful to solve for u in terms of x

[vestal hollow]

This would be convergent under ratio test right?

[glass lichen]

you can use ratio test to see if it converges, yes

[vestal hollow]

I tested (n+1)/(n+1)! * n!/n

Maybe I should put parentheses around that

That simplifies into (n+1)/((n+1)(n!)) * n!/n

Turns into 1/n, limit approaching inf is zero < 1 => abs convergent

[alpine sable]

please what is an ordered set PLEASE HELP

[manic glade]

a set in which the order of elements is specific rather than irrelevant i reckon

https://mathworld.wolfram.com/OrderedSet.html 🤔

[alpine sable]

fuck uni im done

[pallid trout]

This is kind of an odd question, it's not related to any course so it might be a bit vague.
I am playing a game where you combine 2 materials, can honestly be anything, to create a piece of armor. This armor will have 3 important values, Piercing Defense, Slashing Defense and Blunt Defense. When creating the armor, I put in 2 materials (both must be different), then I can put in "extra" materials using a slider, from 0 to 100, this also affects the end result. I know that the armor style that I am using also has an effect on those.
I am trying to figure out the formula, and I have really no idea how many constants or how it might be built. We have hypothesis, but we don't know. Is there a method to trying to basically reverse engineer a formula?

[solar tapir]

Do you have the values?

with different combinations?

[pallid trout]

Yes

Let's define
X = Bone Tissue
Y = Fullgrain leather
An armor with X and Y, with both sliders to 100% = 41.31 blunt, 40.71 Piercing, 42.72 Slashing
An armor with X and Y, with both sliders to 0% = 27.57 blunt, 26.22 piercing, 29.34 slashing

I also did X with 100% and Y with 0% = 34.68, 36.3, 38.12

Since with sliders at 0% we have something, obviously we have constants

So my first idea was a model following
Slashing Defense = First Material Slashing Defense * (1+Slider) + Second Material Slashing Defense * (1+slider)
But when I isolated my 2 variables, it wouldn't work.
Then I added a constant
Slashing Defense = First Material Slashing Defense * (1+Slider) + Second Material Slashing Defense * (1+slider) + Armor Style constants
And this actuallt works very well within ONE combination

[solar tapir]

Looks like a regression problem

[pallid trout]

So to the python machine then? I was trying to solve it on paper since this is kinda fun

Using that last formula, it kinda works, but not 100%

[manic glade]

have you looked for a wiki page on it?

[pallid trout]

So let's say I do D = X(1+s) + Y(1+s) + C and isolate all 3. And then I switch Y for Z, and isolate Z, the further I am from the slider value that I isolated, the more off I am, but very, very slightly

[pallid trout]

I did, thoroughly, people keep that information secret

[solar tapir]

Are there several materials?

[manic glade]

honestly there isnt enough info to even start guessing, you need to also check for the other variables

like same materials but different armor type and same armor type but different materials

and for both of these do the slider checks too

[solar tapir]

Yup, a regression

[pallid trout]

Yeah, I was starting with one step and then I was gonna expand from there

[solar tapir]

With interaction and indicator variables

[pallid trout]

I've done SOME regression ages ago, but it was mostly linear

[pallid trout]

about 100 or so?

[solar tapir]

Holy....

[manic glade]

isolate the variables, change one item see how it affects the result then see if doing the same change affects the result the same way for a different item type, find the additive bonuses the statics and the multiplicative ones

[solar tapir]

This

[pallid trout]

Yeah that's what I did

[solar tapir]

For the 100 types?

*materials

[pallid trout]

No lol

[solar tapir]

That's what he's telling you to do

[pallid trout]

I can't evne get my hand on half of them lol

[manic glade]

not necessarily

but at least like

4 materials and 3 armor types

[pallid trout]

But I've tested it with a handful

[solar tapir]

A representative sample

4 of 100?

[manic glade]

so you can make some base deductions about how things interact

[solar tapir]

Another important thing is

[manic glade]

its unlikely materials change the fomula

[pallid trout]

Well, if the formula is found that works with 4 different materials, it honestly should work with them all after that

[manic glade]

a better material might have higher value but a static bonus will remain a static bonus

generally speaking

hes looking for the formula

[pallid trout]

One thing I know for sure is that different materials just change the coefficient

So if bone tissue is 5 but Tungsteel is 20, it's just that value plugged into the formulla

[solar tapir]

Do you get always get the same stats using the same combination?

[manic glade]

but it depends on the game, its plausible different materials have different types of bonuses and not just values

what game is this even

[pallid trout]

Mortal online 2

[manic glade]

yeah randomness could also be a factor

[pallid trout]

Yes, 100%

There's no randomness

[manic glade]

in which case throw that game into the trash

[solar tapir]

Then it's deterministic

[manic glade]

yuck

[solar tapir]

A good place to start

Is to plot the variables

Using a scatterplot

That will give you hints about the relationship between them

[pallid trout]

Guess I'll have to do that

[harsh cobalt]

is this channel in use ?

[pallid trout]

nah it's good

[harsh cobalt]

im driving myself slightly crazy

with the following question

[next void]

Can someone explain how to solve for X,Y,Z, and W? I am not sure what to do.

[solar tapir]

Dm if you want some day. Looks like something interesting

[solar tapir]

y can be found using the inclusion-exclusion principle

[harsh cobalt]

suppose I have a joint distribution, such that X~uniform distribution a,b and Y ~ uniform distribution c,d. Now I want to find the expectation of X for when Y is < Z

all i do is integrate x f(xy) wrt x wrt y, x from a to b and y from c to Z right?

sorry man this seems to fundamental but its driving me mad

i cant decide if i need to use the conditional distribution or the full distribution

[solar tapir]

The uniform distributions are the marginals of X and Y?

[harsh cobalt]

yea sure

they can just be as simple as

f(x,y) = f(x) f(y)

i don't think that fundamentally affects my question

[solar tapir]

What is Z?

[harsh cobalt]

some arbitrary boundary that does not need to be a parameter

[solar tapir]

Is it a value?

[harsh cobalt]

it doesnt have to be

i am looking for generic result

[solar tapir]

I think you need to refine several things in the problem statement

That Z looks like a value, not a variable

So it should be z

[harsh cobalt]

no

[solar tapir]

And what you need to find looks like $\mathbf{E}[X|Y<z]$

[ocean seal]

Max Hetfield

[harsh cobalt]

nope

i am looking for a generic result

[solar tapir]

This reinforces my point

[harsh cobalt]

not really

since Z could be Y/2 + 1

which will ultimately take the same form

of RV < value

[pallid trout]

Isn't there like a theorem where A ∪ B = A + B - A ∩ B

Something like that?

Been a while

[solar tapir]

That's the inclusion exclusion principle

[pallid trout]

Wouldn't that basically solve his thing?

oh

different people

[solar tapir]

Solves for y, but there are other variables remaining

[solar tapir]

What do you need to find?

[harsh cobalt]

all i do is integrate x f(xy) wrt x wrt y, x from a to b and y from c to Z right?

i dont need to find anything

[solar tapir]

$\mathbf{E}[X|Y>z]$

[harsh cobalt]

im asking a question about methods

[ocean seal]

Max Hetfield

[harsh cobalt]

Now I want to find the expectation of X for when Y is < Z

[solar tapir]

Mate

use mathematical notation

Because one means conditional expectation

For me it looks like you wanna find $\mathbf{E}[X|Y>z]$

[ocean seal]

Max Hetfield

[solar tapir]

If that's the case

Then you need to find $f_{X|Y}(x)$

[ocean seal]

Max Hetfield

[solar tapir]

And you get that using $f_{X|Y}(x) = \frac{f_{X,Y}(x,y)}{f_{Y}(y)}$

[ocean seal]

Max Hetfield

[upper bridge]

how do you answer as question like this

[solar tapir]

???

With a calculator?

[upper bridge]

no calculators allowed

(Make sure your answer is an algebraic expression with square roots but without trigonometric or inverse trignometric functions.)

is what it says

[solar tapir]

Special angles tables then

[upper bridge]

thanks

[granite lily]

How do I do this

[solar tapir]

Have you set the inequality equation?

[granite lily]

No

[solar tapir]

Then do it

[granite lily]

I need help with it

[solar tapir]

OK, let's start with the first part

8 less 4 times the square of a number

Try to state that as an equation

[granite lily]

Bruh 😂😂

Thx

[dusk smelt]

No

[solar tapir]

This is not a site to just throw homework, BTW

Users are expected to show their attempts

[granite lily]

Lmao max u suck

Just be straight forward lmao

[strong furnace]

and do your work for you?

[dusk smelt]

But he can learn from the solution

[granite lily]

It’s practice homie not hw

Yeah

That’s how I learn

[solar tapir]

He will not learn from it

[strong furnace]

5. While asking questions, make sure you mention all relevant details, including the context, what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you. I hope this means something

[solar tapir]

That's like reading a solution manual

[granite lily]

Fuck off max u don’t know my learning strategies

[solar tapir]

<@&268886789983436800>

[granite lily]

Lol why

Someone’s mad

[dusk smelt]

Zuddo, did you learn from my solution?

[granite lily]

Yeah i did

I have two more questions like that and now I know how to do it

[dusk smelt]

That's great

[granite lily]

Yeah I appreciate ur help

[dusk smelt]

Good luck, I'm just trying to help

[granite lily]

Yeah ur doing a great job just max is being a stick up

[solar tapir]

Yeah, I'm sure he will solve the next inequality by himself

[pallid trout]

I figured out the issue I think, but I am stuck in a problem where I always have as many equations as variables

[solar tapir]

Lineal equations?

[pallid trout]

For a material X and Y, if you solve for the change based on slider, such as 40.71 = 2X + 2Y + Constants and 30.63 = X + 2Y + Consants
Then 40.71 - 30.73 = 2X + 2Y + Constants - X -2Y - Constants -> 4.41 = X
Do this with the other and I know that, in this case, the constants sum up to 11.73
In another scenario, Z and Y, I solve for Z and Y (Y is the exact same solved value, as it should be!), the constant is now 11.4

Now, I know someone who said he solved it, but he doesn't want to share it, but he says I am close. So I am thinking it's one constant for each material is added. And it would be D = (1+S_1)*X + (1+S_2)*Y + C_X + C_Y

But the thing is, since those things are constant per material, I always end up with as many equations as variable

So with material X and Y with 0 sliders, itw ould just be D = X + Y + C_X + C_Y and then with Z and Y, D = Z + Y + C_Z + C_Y

So I end up with a bunch of sums of 2 constants,
C(xy) = C_X + C_Y
C(zy) = C_Z + C_Y
C(xb) = C_X + C_B
C(zb) = C_Z + C_B
I can find the difference between 2
Like C(xy) = 11.73 and C(zy) = 11.4
Then C(xy) - c(zy) = C_X + C_Y - C_Z - C_Y
0.33 = C_X - C_Z
Doesn't really help.

I guess I could bruteforce one

The rest would solve itself

[clear citrus]

Write the interval notation for the condition:

5<x

[alpine sable]

Makes no sense

K

Chain rule indefinite integration

[strong furnace]

second line should be 1/2*(4x+5)^-3

[jade spear]

Is there a typo on (b)

I’ve been staring at this for literally hours

v0 is free under the last statement for phi(v0)

It has no quantification

Also I can’t find anything on nLab about a variable being free wrt a substitution using this definition

So I don’t know what they’re actually referring to?

(Perhaps this is a better question for #foundations)

[proud ibex]

i think so!

[jade spear]

Thanks posted it there

[solar tapir]

What have you done?

[shell blade]

ik you have to find the volume of the wooden rolling pin but it gives you a length and radius and no height and i only know how to find the volume of a cylinder using height

[solar tapir]

But you have a relation between the volumes

[shell blade]

the metal cylinder is 2/5 the wooden one

so you have to find the wooden volume first to find the metal volume and then u can find the metals radius with the volume right?

[solar tapir]

Yup

[shell blade]

but how do I find the volume of the wooden cylinder without the height?

[solar tapir]

the height is the length

[shell blade]

is it?

[solar tapir]

Yes

[shell blade]

ohhh cuz its a cylinder and the other is the base

thank you

[solar tapir]

You're welcome

[lean nacelle]

can someone help me please. How do i find the critical points of the function f(x,y)=x^2+3xy-2y^2

[solar tapir]

Find all the points where the first-order partial derivatives are equal to zero or undefined, by solving simultaneously the system of partial derivatives equations

[raw inlet]

can someone help me on this

[solar tapir]

What have you done?

[raw inlet]

i tried converting seconds into minutes then putting that in the r(t) formula

then I took the area of a circle formula and tried to derive it

but i got stuck there

[solar tapir]

Do you know the concept of related rates?

[vivid ocean]

A=pi*r^2
Replace r with 2t^3
Find the derivative and evaluate at t=30

[raw inlet]

ehh somewhat my teacher didnt teach this unit too well

[raw inlet]

okok ill try that

[alpine sable]

how can i know whether to use :

i meant to write "instead of" there, sorry 😅

im still unfamiliar with latex

[dusk smelt]

It's the same thing

[raw inlet]

do you know if radius is in cm or metres?

[alpine sable]

oh...

so i can use either to apply the sine law?

[solar tapir]

Yes

[alpine sable]

oh nice

thanks ^^

[lean nacelle]

please help me. how would i find the critical points for the function f(x,y)=x^2+4y? i found fx=2x and fy=4. so then i set 2x=0 and got x=0. but how do i find y?

[dusk smelt]

4y

For all values of y

[lean nacelle]

what do you mean?

[raw inlet]

ok this is what i did, im still not sure about the units

tho

[dusk smelt]

Why didn't you square the radius

A=pi r²

[raw inlet]

oh whoops lemme fix that

[rocky tusk]

Hey I have a question but it’s a for a very simple problem can I still ask?

I’ll ask but apologies in advance for my stupidity

Can someone tell me what proportion we would use for this

They are similar triangles

[raw inlet]

does this look better?

[dusk smelt]

Yes

[raw inlet]

is it m or cm?

[dusk smelt]

Wasn't given in the question

So no units

[raw inlet]

okok

[quick surge]

ok can anyone help me find the surface area of trapezium

[solar tapir]

There are no critical points for that function, as the system of partial derivatives is not consistent

[dusk smelt]

@lean nacelle 4y is the critical "point"

It is a line, rather than a point

[quick surge]

[dusk smelt]

So for all real numbers of y

@quick surge it's just areas of rectangles combined

What are you struggling with?

[quick surge]

ik the thing is

wait

i dont know whats this

is it 80??

cause like i need to find that area

[tawny gull]

can you guys help my friend im on class rn so ye

[quick surge]

and i only know 1 number

[quick surge]

switch channrels

[tawny gull]

ok

[quick surge]

its used here

@dusk smelt i found F C D E

1/2 x h(a+b)

4(12+22)

136cm^2

[dusk smelt]

Find the height first

20-12

[quick surge]

i did

[dusk smelt]

Then use Pythagoras theorem to find that hypotenuse

[quick surge]

i cant

u dont even have the

[dusk smelt]

The base?

[quick surge]

switch channel;s

[dusk smelt]

That's 20-12

[quick surge]

nonon

to use phy theorm is a^2 = b^2 + c^2

i dont even have b^2 and c^2

[dusk smelt]

Yeah

You want to get the c²

So we need to find a and b first